According to the article, "99 percent of artichokes, 99 percent of walnuts, 97 percent of kiwis, 97 percent of plums, 95 percent of celery, 95 percent of garlic, 89 percent of cauliflower, 71 percent of spinach, and 69 percent of carrots" are produced in our great state. It also links to an Agricultural Statistical Review housed on the Mother Jones website that appears to be documenting 2009, which states, "The state produces nearly half of U.S.-grown fruits, nuts and vegetables."
The rest of the country produces a lot of corn, soybeans and wheat, as well as livestock (which consumes most of that corn and soy). Even so, California's total agricultural receipts, which totaled $38.4 billion in 2009, are by far the highest in the country and are about double the state with the second highest agriculture revenues (Texas). This is obviously due in part to our massive size compared to many other states, but it's also due to the climate and the role agriculture has played historically because of that climate.
The Slate article seems to be focusing on what America's diet and economy would be like if it lost California, which is kind of an odd premise -- what do they expect, that we're going to fall off the country in a giant earthquake? Secede from the nation and hold everyone hostage with our glorious vegetable wealth? Actually, now that I think about it, not such a bad plan. We also have lots of wine to drink, so it could be quite a party.